Question

The angular magnification of a simple microscope can be increased by increasing
the focal length of the lens.
the size of the object.
the aperture of the lens.
the power of the lens.

Answer 1

Hint:The angular magnification depends on the angles subtended by the image and the object at the eye when each is at the least distance of distinct vision. The least distance of distinct vision is known to be $25\text{cm}$ for the human eye. So the angular magnification is found to be inversely proportional to the focal length of the lens.

Formulas used:
-The angular magnification of a simple microscope when the image is at infinity is given by, $m={\displaystyle \frac{D}{f}}$ where $D$ is the least distance of distinct vision and $f$ is the focal length of the lens.
-The angular magnification of a simple microscope when the image is at a near point is given by, $m=1+{\displaystyle \frac{D}{f}}$ where $D$ is the least distance of distinct vision and $f$ is the focal length of the lens.
-The power of the lens is given by, $P={\displaystyle \frac{1}{f}}$ where $f$ is the focal length of the lens.

Complete step by step answer.
Step 1: Express the relations between the angular magnification and the focal length of the lens.
When the image is at infinity, we have the angular magnification as $m={\displaystyle \frac{D}{f}}$ --------- (1)
where $D$ is the least distance of distinct vision and $f$ is the focal length of the lens.
Also when the image is at a near point, we have $m=1+{\displaystyle \frac{D}{f}}$ --------- (2).
Equations (1) and (2) implies that $m\propto {\displaystyle \frac{1}{f}}$ .
As the power of the lens is expressed as $P={\displaystyle \frac{1}{f}}$ , we can conclude that an increase in the power of the lens will increase its angular magnification.

So the correct option is D.

Note:A simple microscope makes use of a converging lens to magnify objects. Increasing the aperture of the lens will result in a corresponding increase in the radius of curvature of the lens. As the radius of curvature of the lens is $R=2f$ , increasing the aperture will increase the focal length as well. From equations (1) and (2) it is clear that the size of the object has no contribution to the angular magnification of the lens. So an increase in the size would not be effective.